Question

18£®£¨1£©´Óºê¹ÛÏÖÏóÖÐ×ܽá³öÀ´µÄ¾­µäÎïÀíѧ¹æÂɲ»Ò»¶¨¶¼ÄÜÊÊÓÃÓÚ΢¹ÛÌåϵ£®µ«ÊÇÔÚijЩÎÊÌâÖÐÀûÓþ­µäÎïÀíѧ¹æÂÉÒ²Äܵõ½Óëʵ¼Ê±È½ÏÏà·ûºÏµÄ½áÂÛ£®
ÀýÈ磬²£¶û½¨Á¢µÄÇâÔ­×ÓÄ£ÐÍ£¬ÈÔÈ»°Ñµç×ÓµÄÔ˶¯¿´×ö¾­µäÁ¦Ñ§ÃèÊöϵĹìµÀÔ˶¯£®ËûÈÏΪ£¬ÇâÔ­×ÓÖеĵç×ÓÔÚ¿âÂØÁ¦µÄ×÷ÓÃÏ£¬ÈÆÔ­×ÓºË×öÔÈËÙÔ²ÖÜÔ˶¯£®ÒÑÖªµç×ÓÖÊÁ¿Îªm£¬ÔªµçºÉΪe£¬¾²µçÁ¦³£Á¿Îªk£¬ÇâÔ­×Ó´¦ÓÚ»ù̬ʱµç×ӵĹìµÀ°ë¾¶Îªr₁£®
a£®ÇâÔ­×Ó´¦ÓÚ»ù̬ʱ£¬µç×ÓÈÆÔ­×ÓºËÔ˶¯£¬¿ÉµÈЧΪ»·ÐεçÁ÷£¬Çó´ËµÈЧµçÁ÷Öµ£®
b£®ÇâÔ­×ÓµÄÄÜÁ¿µÈÓÚµç×ÓÈÆÔ­×ÓºËÔ˶¯µÄ¶¯ÄÜ¡¢µç×ÓÓëÔ­×ÓºËϵͳµÄµçÊÆÄܵÄ×ܺͣ®ÒÑÖªµ±È¡ÎÞÇîÔ¶´¦µçÊÆΪÁãʱ£¬µãµçºÉµç³¡ÖÐÀ볡ԴµçºÉqΪr´¦µÄ¸÷µãµÄµçÊƦÕ=k$\frac{q}{r}$£®Çó´¦ÓÚ»ù̬µÄÇâÔ­×ÓµÄÄÜÁ¿£®
£¨2£©ÔÚ΢¹ÛÁìÓò£¬¶¯Á¿Êغ㶨ÂɺÍÄÜÁ¿Êغ㶨ÂÉÒÀÈ»ÊÊÓã®ÔÚÇáºË¾Û±äµÄºË·´Ó¦ÖУ¬Á½¸ö뮺ˣ¨${\;}_{1}^{2}$H£©ÒÔÏàͬµÄ¶¯ÄÜE₀=0.35MeV×ö¶ÔÐÄÅöײ£¬¼ÙÉè¸Ã·´Ó¦ÖÐÊͷŵĺËÄÜÈ«²¿×ª»¯Îªº¤ºË£¨${\;}_{2}^{3}$He£©ºÍÖÐ×Ó£¨${\;}_{0}^{1}$n£©µÄ¶¯ÄÜ£®ÒÑ֪뮺˵ÄÖÊÁ¿m_D=2.0141u£¬ÖÐ×ÓµÄÖÊÁ¿m_n=1.0087u£¬º¤ºËµÄÖÊÁ¿m_He=3.0160u£¬ÆäÖÐ1uÏ൱ÓÚ931MeV£®ÔÚÉÏÊöÇáºË¾Û±äµÄºË·´Ó¦ÖÐÉú³ÉµÄº¤ºËºÍÖÐ×ӵĶ¯Äܸ÷ÊǶàÉÙMeV£¿£¨½á¹û±£Áô1λÓÐЧÊý×Ö£©

Answer 1

·ÖÎö £¨1£©¸ù¾Ý¿âÂØÁ¦ÌṩÏòÐÄÁ¦£¬½áºÏµçÁ÷±í´ïʽ$I=\frac{e}{T}$£¬¼´¿ÉÇó½â£»¸ù¾Ý¶¯Äܱí´ïʽ£¬½áºÏµçÊÆÄÜ£¬¼´¿ÉÇó½âÄÜÁ¿£»
£¨2£©ÓÉ°®Òò˹̹µÄÖÊÄÜ·½³Ì£¬½áºÏÄÜÁ¿Ó붯Á¿Êغ㣬¼´¿ÉÇó½â£®

½â´ð ½â£º£¨1£©a£®µç×ÓÈÆÔ­×ÓºË×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÓУº$k\frac{e^2}{r_1^2}=m\frac{v_1^2}{r_1}$
$T=\frac{{2¦Ð{r_1}}}{v_1}$
½âµÃ£º$T=\frac{2¦Ð}{e}\sqrt{\frac{mr_1^3}{k}}$
µç×ÓÈÆÔ­×ÓºËÔ˶¯µÄµÈЧµçÁ÷Ϊ£º$I=\frac{e}{T}$
$I=\frac{e^2}{2¦Ð}\sqrt{\frac{k}{mr_1^3}}$
b£®ÓÉa£®¿ÉÖª£¬´¦ÓÚ»ù̬µÄÇâÔ­×ӵĵç×ӵĶ¯ÄÜΪ£º${E_{k1}}=\frac{1}{2}mv_1^2=\frac{{k{e^2}}}{{2{r_1}}}$
È¡ÎÞÇîÔ¶´¦µçÊÆΪÁ㣬¾àÇâÔ­×ÓºËΪr´¦µÄµçÊÆΪ£º$ϕ=k\frac{e}{r_1}$
´¦ÓÚ»ù̬µÄÇâÔ­×ӵĵçÊÆÄÜΪ£º${E_{p1}}=-eϕ=-\frac{{k{e^2}}}{r_1}$
ËùÒÔ£¬´¦ÓÚ»ù̬µÄÇâÔ­×ÓµÄÄÜÁ¿Îª£º${E_1}={E_{k1}}+{E_{p1}}=-\frac{{k{e^2}}}{{2{r_1}}}$
£¨2£©ÓÉ°®Òò˹̹µÄÖÊÄÜ·½³Ì£¬ºË¾Û±ä·´Ó¦ÖÐÊͷŵĺËÄÜΪ£º¡÷E=¡÷mc²
½âµÃ£º¡÷E=3.3MeV
ºË·´Ó¦ÖÐϵͳµÄÄÜÁ¿ÊغãÓУºE_kHe+E_kn=2E₀+¡÷E
ºË·´Ó¦ÖÐϵͳµÄ¶¯Á¿ÊغãÓУºp_He-p_n=0
ÓÉ${E_k}=\frac{p^2}{2m}$¿ÉÖª£º$\frac{{{E_{kHe}}}}{{{E_{kn}}}}=\frac{m_n}{{{m_{He}}}}$
½âµÃ£º${E_{kHe}}=\frac{m_n}{{{m_n}+{m_{He}}}}£¨{2{E_0}+¡÷E}£©$=1MeV
${E_{kn}}=\frac{{{m_{He}}}}{{{m_n}+{m_{He}}}}£¨{2{E_0}+¡÷E}£©$=3MeV
´ð£º£¨1£©a£®´ËµÈЧµçÁ÷Öµ$\frac{{e}^{2}}{2¦Ð}\sqrt{\frac{k}{m{r}_{1}^{3}}}$£®
b£®´¦ÓÚ»ù̬µÄÇâÔ­×ÓµÄÄÜÁ¿$-\frac{k{e}^{2}}{2{r}_{1}}$£»
£¨2£©ÇáºË¾Û±äµÄºË·´Ó¦ÖÐÉú³ÉµÄº¤ºËºÍÖÐ×ӵĶ¯ÄÜ·Ö±ðÊÇ1MeVÓë3MeV£®

µãÆÀ ¿¼²é¿âÂض¨ÂÉ¡¢ÍòÓÐÒýÁ¦¶¨ÂɵÄÄÚÈÝ£¬ÕÆÎÕÅ£¶ÙµÚ¶þ¶¨ÂɵÄÓ¦Óã¬Àí½âÄÜÁ¿ÊغãÓ붯Á¿ÊغãµÄ±í´ïʽ£¬¼°ÖÊÄÜ·½³ÌµÄÄÚÈÝ£¬×¢ÒâÕýÈ·µÄ·ûºÅÔËËãÒ²ÊǽâÌâµÄ¹Ø¼ü£®